Preheat the oven to 180 C. Lightly grease a 23x13cm loaf tin.
In a large bowl, combine flour, bicarbonate of soda and salt.
In a separate bowl, cream together butter and brown sugar. Stir in eggs and mashed bananas until well blended. Stir banana mixture into flour mixture; stir just to moisten. Pour mxture into prepared loaf tin.
Bake in preheated oven for 60 to 65 minutes, until a knife inserted into centre of the loaf comes out clean. Leave to cool in tin for 10 minutes, then turn out onto a wire cooling rack.